"Cette femme est plus âgée que je ne suis."
It's called a "ne" explétif, which means that this adverb is not mandatory and has nothing to do with the negation one ("ne...pas").
It only appears in subordinates parts (after "que") with certain verbs or constructions like the present example.
By the way, the usual form of this sentence is more often : Cette femme est plus âgée que moi.
Yes it is, because "elderly" is a noun, a polite word for "old person". Therefore you cannot use a comparative (more... or less...) with a noun, only with an adjective.
the simple adjective "old" is sufficient.
In French : "vieux" (singular/plural - masculine) and "vieille" or "vieilles" (singular or plural - feminine)
Elderly is an adjective not a noun. "An elder" is a noun. http://dictionary.reference.com/browse/elderly?s=t
Because it's an adjective with 3 syllables it therefore requires the use of most/more/less etc before it when used as a comparative or superlative.
It certainly isn't a very common statement though, so probably not worth including here.